We examine one of the well-known mathematical works of Abraham bar Ḥiyya: Ḥibbur ha-Meshiḥah ve-ha-Tishboret, written between 1116 and 1145, which is one of the first extant mathematical manuscripts in Hebrew. In the secondary literature about this work, two main theses have been presented: the first is that one Urtext exists; the second is that two recensions were written—a shorter, more practical one, and a longer, more scientific one. Critically comparing the eight known copies of the Ḥibbur, we show that (...) contrary to these two theses, one should adopt a fluid model of textual transmission for the various manuscripts of the Ḥibbur, because neither of these two theses can account fully for the changes among the various manuscripts. We hence offer to concentrate on the typology of the variations among the various manuscripts, dealing with macro-changes (such as omissions or additions of proofs, additional appendices or a reorganization of the text itself), and micro-changes (such as textual and pictorial variants). (shrink)

This volume contains the proceedings of three special sessions: Algebra and Computer Science, held during the Joint AMS-EMS-SPM meeting in Porto, Portugal, June 10–13, 2015; Groups, Algorithms, and Cryptography, held during the Joint Mathematics Meeting in San Antonio, TX, January 10–13, 2015; and Applications of Algebra to Cryptography, held during the Joint AMS-Israel Mathematical Union meeting in Tel-Aviv, Israel, June 16–19, 2014. Papers contained in this volume address a wide range of topics, from theoretical aspects of algebra, namely group theory, (...) universal algebra and related areas, to applications in several different areas of computer science. From the computational side, the book aims to reflect the rapidly emerging area of algorithmic problems in algebra, their computational complexity and applications, including information security, constraint satisfaction problems, and decision theory. The book gives special attention to recent advances in quantum computing that highlight the need for a variety of new intractability assumptions and have resulted in a new area called group-based cryptography. (shrink)

Solomon's sea (a brass basin used in the First Temple) was discussed in the Yerushalmi Talmud Eruvin 1:5 (as well as in BT Eruvin 14a-b), and it revolved around the shape of Solomon's sea. However, inaccurate volume values of the basin were cited in the Yerushalmi. The aim of this article was to offer a new explanation for one problem arising in connection with these values. The setting of this study was the inaccurate volume values of the basin appearing in (...) the Yerushalmi. The background of the issue at stake is the fact that Jewish scholars cannot accept that Scripture contains discrepancies (cf. BerR. 4:6). Our methods were to review the different explanations given by different commentators and to introduce a discussion by R. Avraham Ben Hiyya ha-Nassi and the Book of Tashbetz dealing with an explanation of verses related to the basin's shape. We suggested a new idea based on the above-mentioned discussion: by reducing the basin's width by one handbreadth as the verse states, one could reach exactly the values appearing in the Yerushalmi for the volumes of a squared basin and a circular basin. Based on our suggestion, one could settle the volume values appearing in the Yerushalmi without correcting them. CONTRIBUTION: The key insight was that one could settle the volume values appearing in the Yerushalmi without correcting them. This insight was connected with the textual history of the Rabbinic literature, which exactly fit HTS's scope. (shrink)